Fundamental discoveries in mechanics in recent decade or so

“We seek papers from researchers in all disciplines. Mechanics appeals to talents of all kinds. Good mechanics has long been created by people from many fields, by Galileo, Newton, Maxwell and Faraday, as well as by Watt, Darwin, Wright brothers and Whitesides. People make discoveries in mechanics often when doing something else (e.g., in seeking evidence for the existence of God, in building cathedrals, in flying airplanes, in laying transatlantic telegraph cables, in fabricating microprocessors, in watching cells move, in fracking for gas, in inventing optical tweezers, in creating soft lithography, in developing wearable or implantable electronics). Mechanics discovered in one field invariably finds applications in other fields.”

Here I would like to give several examples of papers published in recent decade or so. I will link each paper to its citations on Google Scholar, so that you can have an overview of the influence of the paper on other researchers.

Tissues of animals and plants are mostly hydrogels, mixtures of macromolecules and water. Hydrogels combine the attributes of both solids and liquids: the network of macromolecules provides resistance to deformation, whereas water enables the transport of solutes. Recent decades have seen applications of engineered hydrogels, such as contact lenses and superabsorbent diapers. Most hydrogels are brittle. Think of tofu and Jell-O. This paper shows that double-network hydrogels, suitably made, are very tough. This discovery has led to a worldwide search for all ways to make hydrogels tough, all possible applications of touch gels, and mechanistic understanding of tough, soft materials. This paper, as well as its influence on researchers in many disciplines, reminded me of a paper published in 1975, Ceramic Steel, which launched a worldwide search for tough ceramics.

On receiving an electrical signal from the brain, a muscle deforms. This electromechanical transduction has long been an inspiration for the development of actuators. Voltage-induced deformation is small in most materials. Piezoelectric ceramics, for example, can typically achieve a voltage-induced strain less than 1%. By contrast, a muscle can achieve a strain about 50%. This paper shows that elastomers can achieve voltage-induced strain greater than 100%. This discovery has created a field of study, and is finding commercial applications. In 2011, I wrote a post entitled From Esoteric Research in Continuum Mechanics to first Commercial Product of Dielectric Elastomer Transducers (1956-2011). The year 1956 marked the publication of Toupin’s paper, The Elastic Dielectric.

Batteries have enabled the wireless revolution, and are under intense development for electrical cars and smart grids. Lithium-ion batteries require materials that absorb a lot of lithium. Carbon is commonly used as anodes. Each carbon atom can accommodate up to ⅙ lithium atoms. By contrast, each silicon atom can accommodate up to 4.4 lithium atoms. Silicon, however, is not commonly used in commercial lithium-ion batteries. The difficulty has been known for decades. On absorbing a large amount of lithium, lithiated silicon swells greatly, leading to fracture. This paper shows that silicon nanowires can absorb a lot of lithium without fracture. This discovery has led to a search for nanostructured electrodes and their commercial applications. The discovery has also reminded mechanicians how poorly we understand coupled deformation, growth, transport, and fracture, and has stimulated a lot of catching-up research in mechanics.

When a slender column is compressed beyond a critical load, the homogeneous deformation becomes unstable, and the column buckles. This elastic instability, as well as many others, has long been analyzed by superimposing a field of small strain on the homogeneous state. Such an analysis, for example, led Biot (1963) to conclude that a block of rubber compressed beyond a critical strain would form wrinkles. His analysis were refined by many others in later years. Biot and his followers have ignored an experimental fact: wrinkles on compressed rubber blocks have never been reported. What a block of rubber does under compression is to form creases, localized regions of self-contact. Hohlfeld and Mahadevan made a theoretical discovery: wrinkles and creases are two distinct types of elastic instability. Whereas wrinkles bifurcate from a homogeneous state by a deviation small in strain, creases bifurcate from a homogeneous state by a deviation small in region. For a block of rubber under compression, the critical strain for the onset of wrinkles is larger than that for the onset of creases. This discovery is permeating into the fabrics of mechanics.

What do you think of these papers? Has your work been influenced by these papers? What are other examples of recent fundamental discoveries in mechanics?

Origami, traditionally the art of paper folding, has been applied to some engineering applications based on its principle of creating 3D structures from 2D sheets through a high degree of folding along the creases. The geometrical and mechanics responses of origami structures mainly depend on the way of folding, not the material properties of the paper itself, which makes origami a mechanical metamaterial. In this paper, a particular origami pattern, namely Miura-ori, was examined as mechanical metamaterials. Specifically, the authors found that in-plane and out-of-plane Poisson’s ratios are equal in magnitude, but opposite in sign, independent of material properties. The effective bending stiffness is found singular. This work has inspired my group to work on the similar topic of origami as mechanical metamaterials (including extremely strong load bearing capability), and some other related work (such as the effect of defects on Miura-ori).

When a crystal deforms plastically, phenomena such as dislocation storage, multiplication, motion, pinning, and nucleation occur over the submicron-to-nanometer scale. Here we report measurements of plastic yielding for single crystals of micrometer-sized dimensions for three different types of metals. We find that within the tests, the overall sample dimensions artificially limit the length scales available for plastic processes. The results show dramatic size effects at surprisingly large sample dimensions. These results emphasize that at the micrometer scale, one must de. ne both the external geometry and internal structure to characterize the strength of a material.